As for the joint masters programs:
The Master of Arts in Social Sciences, i.e. A.M. Social Sciences, is not that hard to get into, and has almost no set requirements. If you are looking to go to a PhD program in history, sociology or the like, the requisite number of graduate courses and your performance in them could help you a fair amount in admission. I would wager the cut is around a 3.3 generally and a 3.5 in your social science courses to have a shot. Extracurricular experiences will not matter since it is an academically oriented, graduate school provisioned degree. The people who are really successful in this program continue on to higher studies in some form, e.g. PhD, MD, JD. It is a huge program by student size, but you get out of it what you put into it since it is very student driven.
The Master of Public Policy, which has concentrations like public finance but not official majors, looks for the well-rounded student in all aspects. You should have some foreign language skills, a bundle of relevant internships, and at least a 3.3. or so. In general however, the Harris School is not consider tops for public policy, so students who qualify usually qualify just wait to go to the leading schools in the field such as Johns Hopkins (SAIS), Harvard (KSG), Columbia (SIPA), Tufts (Fletcher) or Princeton (WWS). It also is a professional school versus a traditional graduate program, so there is something to be said that students without full time work experience might find the student body somewhat unappealing.
The Master of Arts in International Relations, i.e. A.M. International Relations, is far more selective. You would need something like a 3.5 generally and likely more towards a 3.6-3.7 in a social science major. A working knowledge of a relevant language is pretty much expected. It has an excellent placement record in both the public and private sector, and is known for being quite difficult.